The correct answer for the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x is 128/3 * π.
Volume of Solid of Revolution by Shell method is given by
V = 2π * integrate x(height) dx Here, height = 4x-x2
(1)& x-varies from x = 0 to x = 4 then from eqn(1) V = 2π * integrate x(4x - x ^ 2) dx from x = 0 to 4 = 2π * integrate (4x ^ 2 - x ^ 3) dx from x = 0 to 4
Basic Rule(1) ∫ x^n dx =x^ n+1/ n+1
V=2 π [4((x ^ 3)/3) - (x ^ 4)/4] 0 ^ 4 =2 π[ 4/3 x^ 3 - x^ 4/4 ] 0 ^ 4
V = 2π [4/3 * 4 ^ 3 - (4 ^ 4)/4} - 0]
V = 128/3 * π.
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What fraction of the mass of the milky way galaxy is in a form that astronomers have been able to see?
The astronomers have been able to see a 10% of the milky way galaxy's mass
The Milky Way is a large spiral galaxy where the solar system and the Earth are located. It takes its name for the irregular luminous band of stars and gas clouds that stretches across the sky as seen from Earth. According to astronomers, it has a mass of 10¹² solar masses and, by its shape, it is a barred spiral galaxy.
What is the galaxy?It is a large area of gas, dust and billions of stars and their solar systems all held together by gravity that makes up a universe.
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5) In the picture to the right, a wave source is
moving to the right. Measure the wavelengths
recorded by observer A, on the left, and
observer B, on the right.
Do this by measuring 5 wavelengths and
dividing by 5 to get a precise average.
Answer: most likely its going to be 5
Explanation:
because you have to keep it the same
7. 122 10 292 252 Fig. 6.31 a The effective resistance of the circuit shown in the figure above is ? NE
R1+R2+R3 =1+1+1=3 is used to represent the circuit's overall resistance.
The 3 resistors on the upper side of the circuit are linked in series in this instance, and the total resistance R1 is expressed as 1+1+1=3.
The combined resistance R2 is expressed as 2+2+2=6 due to the series connection of the three 2-ohm resistors on the lower part of the circuit. The intermediate resistances R1, R2, and 2 are linked in parallel. This parallel connection's total resistance, R3, is therefore represented as 2/1+ 2/1+ 6/1 = 1/1=1 ohm.
In other words, the closed loop's resistance is decreased to 1 ohm.
Now, R1+R2+R3 =1+1+1=3 is used to represent the circuit's overall resistance (R).
As a result, the resistance in the circuit from point A to point B is 3.
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Write down the names of three mar-made devices in everyday use that depend,
for their action, upon the moments of forces.
Answer:
Scissors
Tap
Spanner
Explanation:
What happens to most of the neutrinos produced by the nuclear reactions in the core of the sun? group of answer choices
The neutrinos produced by the nuclear reactions in the core of the sun escape from the sun into space.
The neutrinos produced by the nuclear reactions in the core of the sun is called solar neutrinos. These solar neutrinos are the decay product of nuclear fusion reaction in the sun.
These neutrinos then gets released into space which also reaches earth as light and heat.
Therefore, the neutrinos produced by the nuclear reactions in the core of the sun escape from the sun into space.
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Find an equation of the normal line to the curve y = x that is parallel to the line 2x y = 1.
The equation of the normal line is y = - 2x + 3
We know that,
The equation of normal line given of the curve is given by
( y - [tex]y_{1}[/tex] ) = m ( x - [tex]x_{1}[/tex] )
Given that,
Equation of curve is y = [tex]\sqrt{x}[/tex]
Equation of the line parallel to the normal line of curve is 2x + y = 1
The slope of normal is same as that of the line parallel to it. So,
2x + y = 1
y = - 2x + 1
On differentiating both sides by x,
dy / dx = - 2
which is the slope of normal line
To find slope of the curve,
y = [tex]\sqrt{x}[/tex]
y = [tex]x^{1/2}[/tex]
dy / dx = 1/2 x
which is the slope of the curve.
Since the curve and its normal line is perpendicular,
[tex]m_{1} m_{2}[/tex] = -1
-2 * 1/2 x = -1
x = 1
At x = 1,
y = [tex]\sqrt{1}[/tex] = 1
The point is ( 1 , 1 )
The equation of normal line given of the curve is
( y - [tex]y_{1}[/tex] ) = m ( x - [tex]x_{1}[/tex] )
y - 1 = - 2 ( x - 1 )
y = - 2x + 3
Therefore, The equation of the normal line is y = - 2x + 3
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